Factor completely. $7x^5-21x^4+14x^3=$
As a first step, let's see if there's a common factor we can factor out. Greatest common factor The greatest common factor of $7x^5$, $-21x^4$, and $14x^3$ is $7x^3$. Let's factor $7x^3$ out of $7x^5-21x^4+14x^3$ : $\begin{aligned} &\phantom{=}7x^5-21x^4+14x^3 \\\\ &=7x^3(x^2)+7x^3(-3x)+7x^3(2) \\\\ &=7x^3(x^2-3x+2) \end{aligned}$ We can keep factoring the expression by factoring $x^2-3x+2$. Factoring $x^2-3x+2$ $x^2-3x+2=(x-1)(x-2)$ Putting it all together $\begin{aligned} &\phantom{=}7x^5-21x^4+14x^3 \\\\ &=7x^3(x^2-3x+2) \\\\ &=7x^3(x-1)(x-2) \end{aligned}$ In conclusion, this is the completely factored expression: $7x^3(x-1)(x-2)$